WSPC04651

• File Number: 8062
• Description: Federal Water Rights - Colorado Litigation - National Forest ISF Claims - Division 2
• State: CO
• Basin: Statewide
• Date: 9/17/1997
• Title: Materials of Interest - Effective Discharge and the Design of Channel Maintenance Flows for Gravel-Bed Rivers
• Water Supply Pro - Doc Type: Report/Study

O(J2094

]56 EFFECTIVE DISCHARGE AND CHAKNEL-MAINTEI'Aj\;CE FLOWS

where W'i = [q" (-,'" - 1)] I ffi gl." (RS)"'], <p, = T," / T'i"
q" is the volu=etric bedload transpon rate of the i>
panicle fraction per unit width of channel, f, is the percent
of bed particles in the i~ fraction, and g is lhe acceleration
of gravity.
An essential aspect of this approach was the development
of a refereDce dimensionless shear stress. TUtJ. such that 1:rl
= f (d/d",) where d, is the diameter of particles of the I"'
siu fraclion of bed material and d" is the median p:ll'licle
diameter of bed materia!. Parker er al. [1982J found that
the Use of <P,. rather than T, . resulted in a similanry
collapse, so that W', is approximately a single valued
function of cili. The Parker bedload function for the domain
<l>i > 1.65 was derived by tining cili and W', to the Einstein
bedload function. For the domain 0.95 < <1>, < 1.65, the
Parker bedload function was derived from bedload
transpon rales measured in Oak Creek [Milhol/S. 1973],
As formulated, equation (I) should apply to any mixture
of gravel-sized material. from uniform to poorly-sorted. so
long as the reference shear stress COlTe<tl y represents the
response of the bed material to the fluid forces (Le. when
</>i = I, then W'i = 0.0025). Therefore, equation I should
be generally applicable. The relation T, = f(dld,,),
however, may vary from stream to stream depending upon
the narure of the bed material, particle size-distribution,
shape and packing. The extremely steep slope of the ell, vs
W'; relation. when <P, ~ 1.65, however. means that
relatively small errors in the reference shear SIless, T '" .
will lead to substantial errors in thc predicted bedload
transport rate. Thus, determination of the correct values of
T',; for a given mixture of bed particles is essential.
especially when calculating IlUl'ginal bedload transport .
rates.
Parkl!r er al. [1982] detennined the dependence of r',; on
did", for Oak Creek by calcu]ating the value of r"" at a
dimensionless transport rate of W'i = 0.0025. The panicle
size distribution of subsurface bed material Was used for
most of the analysis of Oak Creek. Their approach.
however, is not limited to the subsurface material. The size
distribution of surface bed material can be used, and is
equally valid [Andrews and Parker, 1987]. The median
particle size of surface bed material is used to scale the
relative partiele protrusion because it represents the
assemblage of bed panicles from whicb the bedload
material is derived, [Wiberg arui Smirh, 1987, Wilcock aNi
McArd.ell. 1993, and Andrews. 1994]. This approach avoids
the need to assume that the partide size distribution of
bedload and subsurface material are similar.
WI/cock aNi Sourlu2rd [1988]. Kuhn/e [1992], and
AllIirews [1994] bave taken a slightly differem approocb
than Parle.T er al. [1982] used to determine the function r"

.00d

0991 86r OL6131

= f(did,,). Inst....d of calculating the value of T'" at W'; =
o 00" 5 thev varied r'. to obtain the best fit of equauon I
. ...." l\ '111 '
to a wide range of measured transport rates of each I Size
fraction. Bedload transport rates have been measured at
three of the river reaches seleeted for this aIlalysis, Middle
Boulder Creek at Nedcrland. ufthand Creek near Boulder.
and South Fork Cache La Poudre River near Rustic.
Using these measurements. the variation of T'" with (did,,)
was determined for each site. The empirically determined
functions. T'" = f(d/d,.,). are shown in Figure 2 together
with the previously determined functions for Oak Creek.
[Parkl!r er al.. ]982] and Sagehen Creek [Andrews, 1994].
The tespective equations are

T'i ~ 0.033 (d/d,,)"''''

(2)

for Oak Creek.

- ~ 00384 (dId ).....'
T ri' t ~o

(3)

for Sagehen Creek near Truckee, CA,

T, ~ 0.0354 (did,,)"''''

(4)

for Middle Boulder Creek at Nederland,

T'ri = 0.0376 (did,,).....

(5)

for Lefthand Creek near Boulder,

T'ri ~ oms (d/d,,).....,

(6)

for the South Fork Cache La Poudre River near Rustic.
Among the five relations, the one determined for Middle
Boulder Creek at Nellerland, is the nearest to an "average'
relation over the range of (d;fd,.,) values. For a given ratio
(dldso), values of the referenced dimensionless shear stress
determined for the 5 streams vary no more than :!: 10
percent from the Middle Boulder Creek relation. see Fig.
ure 2.
Bed-material transport rates for particle size fraclions
from 4 11WI.180 mm over rhe range of recorded discharges
were computed for the 17 sites using the Parker bedload
function. The reference shear stress function, equation 5,
determined for Middle Boulder Creek was applied for all
sites, except Lefthand Creek and the South Fork Cache La
Poudre wh= the site-specific functions w= applied.
Sensitivity of the computed magnirudc and frequency of
bed.material transport to uncertainty in the measured reach
hydraulic charaeteristics and the streamflow regime due to
an insuffieiem period of record were evaluated using the

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